Lecture 4 BJT Small Signal AnalysisJ g y

Present by : Thawatchai ThongleamPresent by : Thawatchai ThongleamFaculty of Science and TechnologyN kh P h R j bh U i iNakhon Pathom Rajabhat University

BJT Small Signal Analysis

OutlineBJT as AmplifierBJT as AmplifierSmall Signal Model

The π-ModelThe π Model The T-Model

Small Signal Analysis g yCommon Emitter (CE) AmplifierCommon Base (CB) Amplifier( ) pCommon Collector or Emitter FollowerBJT Digital LogicJ g g

Introduction Amplifier types

Voltage AmplifiersHigh input resistanceLow output resistanceR

oR

vA oviv p

i

ov v

vA =

iR ivovA oi

Current Amplifiersiv

Low input resistanceHigh output resistance

R RiA viv g p

i

oi i

iA =

iR oRiisiA oviv

i

Transconductance AmplifiersHigh input resistanceHigh output resistanceHigh output resistance

oiA =

iR oRimvG oviv

Transresistance Amplifiersi

G vA =

Low input resistanceLow output resistance

oR

iR Low output resistance

oR

vA =

iR imiR oviv

iR i

Introductionใชว้ธิีการ superposition วเิคราะห์วงจรขยายวเิคราะห์การไบอสัแรงดนักระแสตรงวเคราะหการไบอสแรงดนกระแสตรง

T i t lifi (b) Th i it f ( ) ith thTransistor as an amplifier. (b) The circuit of (a) with the signal source vbe eliminated for dc (bias) analysis.

Transfer characteristic of amplifier circuitการไบอสัแรงดนักระแสตรงหมายถึงออกแบบแรงดนักระแสตรงที่เหมาะสมใหก้บัวงจรขยายเพื่อขยายสญัญาณโดยไม่ผดิเพี้ยนญญ

ภาพที่ 4.26 (a) Basic common-emitter amplifier circuit. (b) Transfer characteristic of the circuit in (a).

Equivalence amplifier circuit

CC

1 C

C

1 C

BC1

2

Bi

o

E

2

Figure 5 27 Circuit whose operation is to be analyzed graphicallyFigure 5.27 Circuit whose operation is to be analyzed graphically.

Small Signal Model of the BJT

The amplifier circuit of Fig. 5.48(a) with the dc sources (VBE and VCC) eliminated (short sources (VBE and VCC) eliminated (short circuited). Thus only the signal components are present Note that this is a representation are present. Note that this is a representation of the signal operation of the BJT and not an actual amplifier circuitactual amplifier circuit.

ภาพที่ 4.50

The Hybrid- π Model ∞=or

BJT as a voltage-controlled BJT as a current-BJT as a voltage controlled current source (a transconductance amplifier)

BJT as a currentcontrolled current source (a current amplifier)(a transconductance amplifier) (a current amplifier).

The Hybrid- π Model ∞≠or

BJT as a voltage-controlled BJT as a current-BJT as a voltage controlled current source (a transconductance amplifier)

BJT as a currentcontrolled current source (a current amplifier)(a transconductance amplifier) (a current amplifier).

Small Signal Analysis

Linear operation of the i ll i ltransistor: small-signal

•vbe triangular waveform is superimposed on dc voltage VBE.

•Collector signal current ic, also of triangular waveform,

i d h dsuperimposed on the dc current IC.

•Ic = gm vbe, where gm is the slope of the ic - vBE curve at the bias point Qbias point Q.

Small Signal Analysis Signal Waveforms

Small Signal Analysis

Ω=== 8.10)99.0/3.2(

25mA

mVIVr

E

Te

VmAmVmA

VIg C

m /9225

3.2===

mVVT 25

Ω==β

= k091100r Ω===π k09.192g

rm

Ex 4.1 ใหเ้ขียนวงจรเทียบเคียงของทรานซิสเตอร์และหาค่า gm , roใ ป ี่และ rπ ของวงจรในรูปที 4. VA = 100

ΩΩ F5μ=

IC

IΩΩ F5μ=

IC

I100=β

F5μ

IB100=β

F5μ

IB

μμ

Single Stage BJT Amplifiers

Common Emitter (CE) AmplifierC B (CB) A lifiCommon Base (CB) AmplifierCommon Collector or Emitter Follower

Measurement of input and output impedances.

Fi M f ( ) i d (b) i dFigure Measurement of (a) input and (b) output impedances.

BJT small signal characteristic

Figure Concept of impedance seen at a node.

Common Emitter (CE) Amplifier

R

CCV

IB C

C

BR ov

1C

2C

iv

CR CI

BI o

vgm

obe

CRBRiB

E

1iv o

Ei

Find Av

ORi

πvvi = (1)outm

out

inv RG

VVA −==

( )Como Rrvgv //π−= (2)out

shortm V

IG =inV

CE

thus( )Comi

ov Rrg

vvA //−== (3)

∞≅orAssume Co RR ≅ (7)iv

o

Thus Riv

π= r//RR Bi

i(5)Cmi

ov Rg

vvA −=≡

oCo r//RR = π≅ rR i (8)(6)oCo (6)

แรงดนัเอาตพ์ตุของวงจรขยายแบบอิมิเตอร์ร่วมกลบัเฟสกบัแรงดนัอินพตุ 180 องศาุ ุ

Common Emitter (CE) Amplifier with RE

πvgm

B CCR

CCV

CI

πr orπgm

ovπvCRBR

ivB

C

BR ov

1C

2C

ivBI

EORiR

ERE

ER EI

(1) (3)outmout

inv RG

VVA −==

( )( )Cbemo

v R1rIRvg

vvA

+β+−==

(2)

out

shortm V

IG =

( )( )Ebi R1rIv +β+π

inV

Find Ro

Short vi and open gmvbe

r rπvgm xI

v

B C

πr orπvCRBR

Vx

EOR

ER E

Co RR ≅

VSmall Signal Analysis (CE)

1R CR

CCV

CIvg

B C1R CR

BC

1C 2CBIiv

ovπr or

πvgm

ovπvCR

2Riv 1R

2R ER

E

3C

EORiR

thus

πvvi =Find Av

( )Como

v RrgvA //−==(1) (3)πi

( )Como Rrvgv //π−=

( )Comi

v gv

(2)

( )

Small Signal Analysis (CE)

oCo rRR //= (4)∞≅orAssume

Co RR ≅ (5)

vthus

Cmi

ov Rg

vvA −=≡ (6)

πrRRRi //// 21=Thus Ri

(7)πi 21

Common Emitter (CE) Amplifier

CE grounds emitter, also ll d “b ” itcalled “bypass” capacitor

Small Signal Analysis

Replace BJT with hybrid π equivalent.

( )Comi

ov Rrg

vvA //−==outmv RGA =

mm gG −=

RR //i RrvR //==

Coout RrR //= Bi

in Rri

R //π==

Ex4.3 Find Av, Ri and Ro on amplifier circuit VA = 100

ΩΩ F5

ICΩΩ F5

ICΩ

100β

Ω F5μ=

IB

Ω

100β

Ω F5μ=

IB100=β

F5μ100=β

F5μ

Ex4.4 Find Av, Ri and Ro on amplifier circuit VA = 100

CC

B2

C ΩΩ F5μ=

BC

1

2 F5μ

80=βEF5μ

80=β

E 3ΩF10μ

Ex4.5 Find Av, Ri and Ro on amplifier circuit at VBE = 0.7 and β 100β=100 VA = 100

Ex4.6 Find Av, Ri and Ro on amplifier circuit VA = 100

CC

1 C ΩΩ

C

o

100=βB

C1 2

Bi

2 E

E

Ω Ω3

Common Base (CB) Amplifier

CI

CCV

πvgm

B C

1R CR

C3C2C

BI

C

ovπr or

πgm

ovπv

E

CR21 // RR

B

E

3C BI

sR1CE

outRivER

ev

2R ER sv

inR

Small Signal Analysis (CB)

Thus Ri and Ro

Ein Rg

R //1= (7)

mg

RR Cout RR = (8)

แรงดนัเอาตพ์ตุของวงจรขยายแบบเบสร่วมมีเฟสเดียวกบัแรงดนัอินพตุ

Ex4.7 Amplifier circuit at IC = 2 mA and VC = +5 V VA = 100Fi d R R A R d RFind RC , RE , Av, Ri and Ro

CCV = + 12 V

ΩC

CC

1R CR

C

ΩΩ

C2C o

470 uFB

E

3C B470 uF

470 uFsR1C

2R ERΩ 500Ωs

1 Vp

470 uF

1 kHz

Ex4.8 Amplifier circuit at IC = 2 mA and VC = +5 V VA = 100Fi d R R A R d RFind RC , RE , Av, Ri and Ro

100=β

Ex4.9 Find Av, Ri and Ro on amplifier circuit at VE = -0.7 and β 50β=50 VA = 100

Common Base (CB) Amplifier

The common-base amplifier. (a) Circuit. (b) Equivalent circuit obtained by replacing the BJT with its T modelcircuit obtained by replacing the BJT with its T model.

Small Signal Analysis (CB) Ex 4.10 จากวงจรขยายเบสร่วมโดยใชท้รานซิสเตอร์ชนิด PNP มี β = 50 ให้ัหาอตัราขยายของวงจร VA = 100

Common Collector Amplifier or Voltage Follower

B CCCV

πr orπvgm

πvBRvBR

CI

Eiv

o

BC

E ov

1C

2C

ivBI

iRER

ibR e ovE ov

ER EI

1≅vA

Find Ro with short vi

Thus RxI

π= r//RR Eo

Thus Ro

ERπrx

x

πEo

Thus R

Bibi R//RR =

Thus Ri

วงจร Emitter-Follower ถกนาํไปใชเ้ป็นวงจรภาคเอาตพ์ตของวงจรขยายที่วงจร Emitter Follower ถกูนาไปใชเปนวงจรภาคเอาตพตุของวงจรขยายทตอ้งการขบัโหลดที่มีค่าความตา้นทานตํ่ามาก

Common Collector Amplifier or Voltage FollowerCC

B C

1R πr orπvgm

πv2R

iv 1R

BC

E

1CBIi E

iR RoI

v

ER2R

E

2CEI

o

iRER

eI ov

EI

Emitter-Follower

Th ll t itt f ll lifi ( )The common-collector or emitter-follower amplifier. (a)Circuit. (b) Equivalent circuit obtained by replacing the BJT with its T model.with its T model.

( ) Th i i d h h i i ll l i h R(c) The circuit redrawn to show that ro is in parallel with RL.

(d) Circuit for determining Ro.

Ex4.11 Find Av, Ri and Ro on amplifier circuit VA = 100

CC

RCI

100 k

BC

BR

1CiBI

100 kΩ

E o2C

R I RER EI1 k Ω

LR 1 k Ω

Ex4.12 Find Av, Ri and Ro on amplifier circuit VA = 100

EEV = -5 V

2C

ER 3.3 kΩ

i BE

o

1C

2C

R100=β

BR

1 kΩC

LR100 kΩ 1 kΩ

CCV = +5 V

Ex4.13 Find Av, Ri and Ro on amplifier circuit VA = 100

Ex4.14 Find Av, Ri and Ro on amplifier circuit VA = 100 Ex4.15 Find Av, Ri and Ro on amplifier circuit

เอกสารอา้งอิง (Reference)1. Adel S. Sedra, Kenneth C. Smith “Microelectronic Circuit”2 P l R G d R b G M “A l i d D i f I d 2. Pual R. Gray and Robert G. Mayer “Analysis and Design of Integrated

Circuit” 3. Behzad Razavi “Fundamentals of Microelectronics” 4 รศ สกัรียา ชิตวงศ ์“วศิวกรรมอิเลก็ทรอนิกส์”4. รศ.สกรยา ชตวงศ “วศวกรรมอเลกทรอนกส”